Question: Rewrite the function by completing the square. $f(x)=x^{2}+12x+7$ $f(x)=(x+$
Solution: We want to complete $x^2{+12}x$ into a perfect square. To do that, we should add $\left(\dfrac{{+12}}{2}\right)^2={36}$ to it: $x^2{+12}x+{36}=(x+6)^2$ In order to keep the expression equivalent, we add and subtract ${36}$, not forgetting the expression's constant term, $7$ : $\begin{aligned} f(x)&=x^2+12x+7 \\\\ &=x^2+12x+{36}+7-{36} \\\\ &=(x+6)^2+7-36 \\\\ &=(x+6)^2-29 \end{aligned}$ In conclusion, after completing the square, the function is written as $f(x)=(x + 6)^2 - 29$